Physical interpretation of the Manifold Hypothesishttps://mathoverflow.net/q/351368/56328?stw=2 …
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Finally, we are all on Twitter to exchange ideas and not one-up each other so I hope everyone feels free to share their perspective. :)
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I don't understand the question yet. But one straightforward thought on neural manifold: Bottleneck-then-expansion strongly favors low-D representations in high-D space (though not guaranteed because of possible temporal multiplexing).
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Here's the problem in two parts: In order to do ML we need to collect a lot of data from a data-generating process so this process must be stable. Empirically we observe that the intrinsic dimension d of the data is generally much smaller than the ambient dimension D. 1/2
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Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces? 2/2
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